* 



OF ARTS AND SCIENCES : MARCH 8, 1864. 247 



already been in great part eliminated (for Polaris, at least) by Groom- 

 bridge himself; for, of the ninety-three observations, forty-one* at least 

 were taken below the pole. Such an error would have been exactly 

 eliminated had one half of the observations been made below the pole. 



There are some smaller discrepancies in the reduction to 1850, 

 whose origin it is not easy to trace. 



All the larger corrections to be made are of negative sign, and refer 

 to the earlier part of the observations, so that, if they were made, the 

 resulting proper motion would be larger algebraically ; while the result 

 for the mean of the dates for which the star's A. R. is correctly given, 

 in the original investigation, would not be much altered, as the follow- 

 ing numbers show. 



B — G = 0^35 + 0^02o (t — 1855). 

 N—G = 0.64 -1-0.037 (t — 1855). 



B, G, N, denote respectively Bessel's, Dr. Gould's, and my own f 

 A. R. of Polaris, for the time t, but referred to the equinox of 1855. 

 In Table I. A a denotes Bessel's discrepancy from observation ; A' a, Dr. 

 Gould's ; A" a, my own ; C. — 0. being taken of an opposite sign to the 

 residuals of §§ 2, 3. 



I have used Dr. Gould's formula, depending on the powers of the 

 time. It is not, however, consistent with the trigonometrical compu - 

 tation from his own elements ; which would deviate more largely from 

 observation. 



The sura of the squares of the discrepancies is, 



For B, 12.88; excluding Piazzi and Groombridge, 8.75 

 « G, 21.91 ; " " " " 15.23 



« N, 10.30; " " " " 7.24 



5. Remarks upon the Tables. 



The authorities for the numbers in Table I. are generally well 

 known; and the following remarks would enable any one to derive 

 essentially the same results in detail as I have given. 



* Philosophical Transactions for 1810. 



t I have obtained by least squares, using the residuals in Table I., the correc- 

 tion N — B = 0".29 -f 0'.012 (t — 1855). I did not think it expedient to use either 

 Piazzi or Groombridge here, on account of the doubt about the position of both 

 their instruments. But they would have tended to make the discrepancy of N 

 from G larger. 



% 



